To our knowledge, Jesus never spoke in tongues. We have so little insight into his personal life that if he did so for his own edification no one was there to witness it. Or if some one was, no biblical author was ever impressed by the Holy Spirit to record it scripturally. Although if some one had witnessed such, I feel fairly certain it would have been recorded in light of Acts 2.
As far as his public ministry goes, we have no incidence recorded in which he ever spoke with tongues. Again in light of Acts 2, had he done so, I feel fairly certain one of the gospel authors would have recorded it. Something so seminal in the birth of the church would have surely had a precedent in the life of Christ recorded if there was one. Alas, the slate is empty.
Regardless, I think the real issue implied by this question is that if Jesus never did, why should we? The answer to that is that regardless of what Jesus' experience was in this respect, the church in its beginnings unanimously spoke in tongues, and the experience was promised to all that followed. For the disciples and those selected to be Apostles by Jesus, the clear choice of God was that every one of them spoke in tongues upon their baptism in the Spirit, even if Jesus did not.
So, the particular experience of Jesus in regards to tongues is not the controlling precedent for those who follow him. Instead, it is the experience of those who first followed him which is the model for their experience. Jesus may have not spoken in tongues, but his followers did, and so can we!